Question

use the graph of the function f to solve the inequality.
(a) f(x) < 0
(b) f(x) ≥ 0
(a) the solution set for f(x) < 0 is
(type your answer in interval notation.)

Explanation:

Step1: Analyze the graph for \(f(x)<0\)

We look at the regions where the graph of the function \(y = f(x)\) is below the \(x -\)axis (\(y = 0\)).
From the graph, we can see that the function \(y=f(x)\) is below the \(x -\)axis when \(x<-3\) or \(-3 < x<1\).

Step2: Write the interval notation

The interval notation for \(x<-3\) is \((-\infty,-3)\) and for \(-3 < x<1\) is \((-3,1)\). Combining these two intervals, since the function is not defined at \(x=-3\) (as \(x = - 3\) is a vertical asymptote), the solution for \(f(x)<0\) is \((-\infty,-3)\cup(-3,1)\)

Answer:

\((-\infty,-3)\cup(-3,1)\)